Rick Cook
REALITY RULES: PICTURING THE WORLD IN MATHEMATICS, VOL. 1: THE FUNDAMENTALS, VOL. 2: THE FRONTIER, John L. Casti, Wiley-Interscience, ISBN 0-471-57021-4 and 0-471-57798-7, $35 each
If the two-volume Reality Rules sounds like gang graffiti, the content is an entertaining but useful graduate-level course in mathematical models--how they work and why they fail. Like all good teaching, these books are lucid and thought-provoking. Like great teaching, they also entertain while showing the world from a new perspective.
Perhaps the most off-putting thing about this work is the table of contents. John Casti includes every trendy topic, from catastrophe theory and cellular automata to genetic programming and sociobiology. And, just to keep modelers humble, he tops it off with a chapter
on the theories of knowledge, citing Kuhn, Sapir-Whorf, Godel, and other members of the currently fashionable pantheon.
In spite of the apparent grab-bag contents, Reality Rules is not another "fluff 'n stuff" popularization. All these fields relate very directly to the business of building good models. Catastrophe theory, Casti says, is useful "in giving us a deeper understanding of what does and doesn't count in the analysis of a particular system."
That statement comes after a solid introduction to catastrophe theory, an examination of how to use it in constructing models, and several pages of a case study showing its use to analyze the growth and collapse of budworm populations. Casti may take you on the scenic route, but he never loses sight of his destination.
For Casti, models are dynamic systems, and model making is the process of mapping reality (or the interesting parts thereof) onto a dynamic system. Ultimately, he says, the success of the model depends on the appropriateness o
f the dynamic system chosen and the fidelity of the mapping. Casti assumes his readers understand vector notation and have a working knowledge of calculus and matrices. Even without that, most of the work is comprehensible, although the more of the math you understand, the more you will profit from the books.
The style, like the math, is easy and informal. Casti is never afraid to substitute a paraphrase where a formal definition or complete proof is unnecessary. If you do computer modeling, these books will save your bacon one day. Meanwhile, they will make you think and entertain you to boot.
Rick Cook uses computer models to help him write science fiction. You can contact him on BIX as "rcook."
Entertaining Math Models
